Operations On sets Exercises 12.1.3

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11.. OQpueardartiaotnics EonquSaettisons eeLleeaarrnn..pPuunnjjaabb

Horizontal lines represent AjB, vertical lines represent AjC and slanting lines represent
(AjB)k(AjC). From fig. (xi) and (xii), it is clear that Aj(BkC) = (AjB)k(AjC). Hence,
distributive law of union over intersection holds.

EXERCISE 1.3

1. Verify the commutative law of union and intersection of the following sets through 
Venn diagrams.
(i) A = {3,5, 7,9,11,13} (ii) The sets N and Z
B = {5,9,13,17,21,25}
(iii) C = {x|x d N/87x718} (iv) The sets is and O
D = {y|ydN/ 97y719}
2. Copy the following figures and shade according to the operation mentioned below
each:

3. For the given sets, verify the following laws through venn diagram.
(i) Associative law of Union of sets.
(ii) Associative law of Intersection of sets.
(iii) Distributive law of Union over intersection of sets.
(iv) Distributive law of Intersection over Union of sets.
(a) A = {2,4, 6,8,10,12}, B = {1,3,5,7,9,11} and C = {3, 6,9,12,15}
(b) A = {x|xdZ/87x725}, B = {y|ydZ/- 2<y<6} and C = {z|zdz/z78}

version: 1.1

13

11.. OQpueardartiaotnics EonquSaettisons eeLleeaarrnn..pPuunnjjaabb

Horizontal lines represent AjB, vertical lines represent AjC and slanting lines represent
(AjB)k(AjC). From fig. (xi) and (xii), it is clear that Aj(BkC) = (AjB)k(AjC). Hence,
distributive law of union over intersection holds.

EXERCISE 1.3

1. Verify the commutative law of union and intersection of the following sets through 
Venn diagrams.
(i) A = {3,5, 7,9,11,13} (ii) The sets N and Z
B = {5,9,13,17,21,25}
(iii) C = {x|x d N/87x718} (iv) The sets is and O
D = {y|ydN/ 97y719}
2. Copy the following figures and shade according to the operation mentioned below
each:

3. For the given sets, verify the following laws through venn diagram.
(i) Associative law of Union of sets.
(ii) Associative law of Intersection of sets.
(iii) Distributive law of Union over intersection of sets.
(iv) Distributive law of Intersection over Union of sets.
(a) A = {2,4, 6,8,10,12}, B = {1,3,5,7,9,11} and C = {3, 6,9,12,15}
(b) A = {x|xdZ/87x725}, B = {y|ydZ/- 2<y<6} and C = {z|zdz/z78}

version: 1.1
  11.. OQpueardartiaotnics EonquSaettisons eeLleeaarrnn..pPuunnjjaabb

Horizontal lines represent AjB, vertical lines represent AjC and slanting lines represent
(AjB)k(AjC). From fig. (xi) and (xii), it is clear that Aj(BkC) = (AjB)k(AjC). Hence,
distributive law of union over intersection holds.

EXERCISE 1.3

1. Verify the commutative law of union and intersection of the following sets through 
Venn diagrams.
(i) A = {3,5, 7,9,11,13} (ii) The sets N and Z
B = {5,9,13,17,21,25}
(iii) C = {x|x d N/87x718} (iv) The sets is and O
D = {y|ydN/ 97y719}
2. Copy the following figures and shade according to the operation mentioned below
each:

3. For the given sets, verify the following laws through venn diagram.
(i) Associative law of Union of sets.
(ii) Associative law of Intersection of sets.
(iii) Distributive law of Union over intersection of sets.
(iv) Distributive law of Intersection over Union of sets.
(a) A = {2,4, 6,8,10,12}, B = {1,3,5,7,9,11} and C = {3, 6,9,12,15}
(b) A = {x|xdZ/87x725}, B = {y|ydZ/- 2<y<6} and C = {z|zdz/z78}

version: 1.1
  11.. OQpueardartiaotnics EonquSaettisons eeLleeaarrnn..pPuunnjjaabb

Horizontal lines represent AjB, vertical lines represent AjC and slanting lines represent
(AjB)k(AjC). From fig. (xi) and (xii), it is clear that Aj(BkC) = (AjB)k(AjC). Hence,
distributive law of union over intersection holds.

EXERCISE 1.3

1. Verify the commutative law of union and intersection of the following sets through 
Venn diagrams.
(i) A = {3,5, 7,9,11,13} (ii) The sets N and Z
B = {5,9,13,17,21,25}
(iii) C = {x|x d N/87x718} (iv) The sets is and O
D = {y|ydN/ 97y719}
2. Copy the following figures and shade according to the operation mentioned below
each:

3. For the given sets, verify the following laws through venn diagram.
(i) Associative law of Union of sets.
(ii) Associative law of Intersection of sets.
(iii) Distributive law of Union over intersection of sets.
(iv) Distributive law of Intersection over Union of sets.
(a) A = {2,4, 6,8,10,12}, B = {1,3,5,7,9,11} and C = {3, 6,9,12,15}
(b) A = {x|xdZ/87x725}, B = {y|ydZ/- 2<y<6} and C = {z|zdz/z78}

version: 1.1
  11.. OQpueardartiaotnics EonquSaettisons eeLleeaarrnn..pPuunnjjaabb

Horizontal lines represent AjB, vertical lines represent AjC and slanting lines represent
(AjB)k(AjC). From fig. (xi) and (xii), it is clear that Aj(BkC) = (AjB)k(AjC). Hence,
distributive law of union over intersection holds.

EXERCISE 1.3

1. Verify the commutative law of union and intersection of the following sets through 
Venn diagrams.
(i) A = {3,5, 7,9,11,13} (ii) The sets N and Z
B = {5,9,13,17,21,25}
(iii) C = {x|x d N/87x718} (iv) The sets is and O
D = {y|ydN/ 97y719}
2. Copy the following figures and shade according to the operation mentioned below
each:

3. For the given sets, verify the following laws through venn diagram.
(i) Associative law of Union of sets.
(ii) Associative law of Intersection of sets.
(iii) Distributive law of Union over intersection of sets.
(iv) Distributive law of Intersection over Union of sets.
(a) A = {2,4, 6,8,10,12}, B = {1,3,5,7,9,11} and C = {3, 6,9,12,15}
(b) A = {x|xdZ/87x725}, B = {y|ydZ/- 2<y<6} and C = {z|zdz/z78}

version: 1.1